Inequalities with 3 5 Solving Variables on Both

Inequalities with 3 -5 Solving Variables on Both Sides Learning Target Students will be able to: Solve inequalities that contain variable terms on both sides. Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality and graph the solutions. y ≤ 4 y + 18 – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 4 m – 3 < 2 m + 6 4 Holt Algebra 1 5 6

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality and graph the solutions. 4 x ≥ 7 x + 6 – 10 – 8 – 6 – 4 – 2 Holt Algebra 1 0 2 4 6 8 10

Inequalities with 3 -5 Solving Variables on Both Sides The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean? 13 < w The Home Cleaning Company is less expensive for houses with more than 13 windows. Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality and graph the solutions. 2(k – 3) > 6 + 3 k – 3 – 12 Holt Algebra 1 – 9 – 6 – 3 0 3

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality and graph the solution. 0. 9 y ≥ 0. 4 y – 0. 5 – 4 – 3 – 2 – 1 Holt Algebra 1 0 1 2 3 4 5

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality and graph the solutions. 0. 5 x – 0. 3 + 1. 9 x < 0. 3 x + 6 – 5 – 4 – 3 – 2 – 1 Holt Algebra 1 0 1 2 3 4 5

Inequalities with 3 -5 Solving Variables on Both Sides There are special cases of inequalities called identities and contradictions. Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality. 2 x – 7 ≤ 5 + 2 x The inequality 2 x − 7 ≤ 5 + 2 x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions. Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Solve the inequality. 2(3 y – 2) – 4 ≥ 3(2 y + 7) No values of y make the inequality true. There are no solutions. HW pp. 197 -199/20 -38, 40 -48 even, 49 -51, 56 -66, 73 -76 Holt Algebra 1

Inequalities with 3 -5 Solving Variables on Both Sides Warm Up Solve each equation. 1. 2 x = 7 x + 15 x = – 3 2. 3 y – 21 = 4 – 2 y y=5 3. 2(3 z + 1) = – 2(z + 3) z = – 1 4. 3(p – 1) = 3 p + 2 no solution 5. Solve and graph 5(2 – b) > 52. b < – 3 – 6 Holt Algebra 1 – 5 – 4 – 3 – 2 – 1 0